In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data-rich ...environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function-valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces efficient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced-form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for postregularization and post-selection inference that are uniformly valid (honest) across a wide range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reducedform functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets. The results on program evaluation are obtained as a consequence of more general results on honest inference in a general moment-condition framework, which arises from structural equation models in econometrics. Here, too, the crucial ingredient is the use of orthogonal moment conditions, which can be constructed from the initial moment conditions. We provide results on honest inference for (function-valued) parameters within this general framework where any high-quality, machine learning methods (e.g., boosted trees, deep neural networks, random forest, and their aggregated and hybrid versions) can be used to learn the nonparametric/high-dimensional components of the model. These include a number of supporting auxiliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) offer a uniformly valid functional delta method, and (3) provide results for sparsitybased estimation of regression functions for function-valued outcomes.
We consider the problem of estimating multiple related Gaussian graphical models from a high dimensional data set with observations belonging to distinct classes. We propose the joint graphical ...lasso, which borrows strength across the classes to estimate multiple graphical models that share certain characteristics, such as the locations or weights of non‐zero edges. Our approach is based on maximizing a penalized log‐likelihood. We employ generalized fused lasso or group lasso penalties and implement a fast alternating directions method of multipliers algorithm to solve the corresponding convex optimization problems. The performance of the method proposed is illustrated through simulated and real data examples.
This paper explains the configuration of the political scenario in Ecuador after the 2021 general elections. The pandemic left a challenging economic and social aftermath that created policy ...challenges for the new government. Guillermo Lasso won the elections securing support from the anticorreísmo front. However, this electoral coalition did not translate into the legislative arena. Lasso addressed policy challenges using political strategies widely used in Ecuador by minority governments during the nineties. We focus on Lasso's attempts to push economic reforms to show how his legislative strategy adapted to the prevailing political conditions, namely: 1) aimed for less ambitious policy goals; 2) used his institutional prerogatives to shape the legislative agenda; and, 3) crafted short-lived and informal agreements in exchange for (political) pork. Complex executive-legislative relations can limit the government's ability to address economic and social problems in the future, which could lead to political and economic instability, as in the past. De facto coalitions are necessary for Lasso yet come at a cost for a government quickly losing support. We also provide an overview of other social problems and policy responses relevant throughout this year. Keywords: fragmented legislature; executive-legislative relations; minority government; coalitions; Guillermo Lasso. Este trabajo explica la configuración del escenario político en Ecuador tras las elecciones generales de 2021. Las consecuencias sociales y económicas del primer año de pandemia representaron un importante desafío para el nuevo gobierno. Guillermo Lasso ganó las elecciones con el apoyo del anticorreísmo, pero este apoyo no se trasladó a la arena legislativa. Lasso asumió los desafíos de política pública recurriendo a estrategias ampliamente utilizadas en Ecuador por gobiernos minoritarios durante los años noventa. Este artículo se centra en los intentos del presidente por sacar adelante sus iniciativas de reforma económica para mostrar de qué manera su estrategia legislativa se adaptó a las condiciones políticas. Específicamente nos enfocamos en explicar cómo el gobierno 1) terminó por configurar una propuesta económica menos ambiciosa, 2) utilizó sus prerrogativas institucionales para moldear la agenda legislativa, y 3) configuró acuerdos informales de corto plazo a cambio de prebendas en la Asamblea Nacional. La complejidad de las relaciones entre el Ejecutivo y el Legislativo limitaron la capacidad del gobierno para resolver los problemas sociales y económicos. Como ocurrió en el pasado, esto podría conducir hacia un escenario de inestabilidad política y económica. Las coaliciones de facto fueron necesarias para Lasso, sin embargo, estas tuvieron costo importante para un gobierno que perdió rápidamente el apoyo de la ciudadanía. Adicionalmente, repasamos los problemas sociales más relevantes de 2021 y la política pública generada para abordarlos. Palabras clave: fragmentación legislativa; relaciones Ejecutivo-Legislativo; gobierno de minoría; coaliciones; Guillermo Lasso
We develop results for the use of Lasso and post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. ...Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post-Lasso in the first stage is root-n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well-approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic "beta-min" conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso-based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post-Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non-Gaussian, heteroscedastic disturbances that uses a data-weighted 𝓁₁-penalty function. By innovatively using moderate deviation theory for self-normalized sums, we provide convergence rates for the resulting Lasso and post-Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that log p = o(n 1/3 ). We also provide a data-driven method for choosing the penalty level that must be specified in obtaining Lasso and post-Lasso estimates and establish its asymptotic validity under non-Gaussian, heteroscedastic disturbances.
In this article, we introduce lassopack, a suite of programs for regularized regression in Stata. lassopack implements lasso, square-root lasso, elastic net, ridge regression, adaptive lasso, and ...postestimation ordinary least squares. The methods are suitable for the high-dimensional setting, where the number of predictors p may be large and possibly greater than the number of observations, n. We offer three approaches for selecting the penalization (“tuning”) parameters: information criteria (implemented in lasso2), K-fold cross-validation and h-step-ahead rolling cross-validation for cross-section, panel, and time-series data (cvlasso), and theory-driven (“rigorous” or plugin) penalization for the lasso and square-root lasso for cross-section and panel data (rlasso). We discuss the theoretical framework and practical considerations for each approach. We also present Monte Carlo results to compare the performances of the penalization approaches.
This paper studies the intrinsic connection between a generalized LASSO and a basic LASSO formulation. The former is the extended version of the latter by introducing a regularization matrix to the ...coefficients. We show that when the regularization matrix is even- or under-determined with full rank conditions, the generalized LASSO can be transformed into the LASSO form via the Lagrangian framework. In addition, we show that some published results of LASSO can be extended to the generalized LASSO, and some variants of LASSO, e.g., robust LASSO, can be rewritten into the generalized LASSO form and hence can be transformed into basic LASSO. Based on this connection, many existing results concerning LASSO, e.g., efficient LASSO solvers, can be used for generalized LASSO.
•A theoretical study is conducted on the generalized LASSO.•A condition is derived to guarantee the equivalence between the generalized LASSO and LASSO.•An upper bound is given on the complexity of the LARS algorithm.•A closed-form solution of the generalized LASSO is derived for several cases.
This article is improved the random forest algorithm by selecting the most appropriate penalized regression methods, and it is tried to improve the post-selection boosting random forest (PBRF) ...algorithm using elastic net regression. The proposed method with the highest efficiency is called Reducing and Aggregating Random Forest Trees by Elastic Net (RARTEN). The introduced method consists of three steps. In the first step, the random forest algorithm is used as a predictor. In the second step, Elastic Net, as a penalized regression method, is applied to reduce the number of trees and improve the random forest and PBRF. In the last step, selected trees are aggregated. The obtained results of the real data and Monte Carlo simulation are evaluated using various statistical performance criteria. The simulation study shows that the RARTEN with 7%, 5%, and 8.5% reduction in the linear, nonlinear, and noise model, respectively improve the accuracy of the traditional random forest and the proposed method by Wang. In addition, this method has a significant reduction compared to other penalized regression methods. Moreover, the real data results show that the proposed method in our study with a reduction of almost 16% confirms the validity of the proposed model.
In this article we study post-model selection estimators that apply ordinary least squares (OLS) to the model selected by first-step penalized estimators, typically Lasso. It is well known that Lasso ...can estimate the nonparametric regression function at nearly the oracle rate, and is thus hard to improve upon. We show that the OLS post-Lasso estimator performs at least as well as Lasso in terms of the rate of convergence, and has the advantage of a smaller bias. Remarkably, this performance occurs even if the Lasso-based model selection "fails" in the sense of missing some components of the "true" regression model. By the "true" model, we mean the best s-dimensional approximation to the nonparametric regression function chosen by the oracle. Furthermore, OLS post-Lasso estimator can perform strictly better than Lasso, in the sense of a strictly faster rate of convergence, if the Lasso-based model selection correctly includes all components of the "true" model as a subset and also achieves sufficient sparsity. In the extreme case, when Lasso perfectly selects the "true" model, the OLS post-Lasso estimator becomes the oracle estimator. An important ingredient in our analysis is a new sparsity bound on the dimension of the model selected by Lasso, which guarantees that this dimension is at most of the same order as the dimension of the "true" model. Our rate results are nonasymptotic and hold in both parametric and nonparametric models. Moreover, our analysis is not limited to the Lasso estimator acting as a selector in the first step, but also applies to any other estimator, for example, various forms of thresholded Lasso, with good rates and good sparsity properties. Our analysis covers both traditional thresholding and a new practical, data-driven thresholding scheme that induces additional sparsity subject to maintaining a certain goodness of fit. The latter scheme has theoretical guarantees similar to those of Lasso or OLS post-Lasso, but it dominates those procedures as well as traditional thresholding in a wide variety of experiments.
Network Inference With the Lasso Waldorp, Lourens; Haslbeck, Jonas
Multivariate behavioral research,
2024-Apr-08
Journal Article
Recenzirano
Odprti dostop
Calculating confidence intervals and
-values of edges in networks is useful to decide their presence or absence and it is a natural way to quantify uncertainty. Since lasso estimation is often used ...to obtain edges in a network, and the underlying distribution of lasso estimates is discontinuous and has probability one at zero when the estimate is zero, obtaining
-values and confidence intervals is problematic. It is also not always desirable to use the lasso to select the edges because there are assumptions required for correct identification of network edges that may not be warranted for the data at hand. Here, we review three methods that either use a modified lasso estimate (desparsified or debiased lasso) or a method that uses the lasso for selection and then determines
-values without the lasso. We compare these three methods with popular methods to estimate Gaussian Graphical Models in simulations and conclude that the desparsified lasso and its bootstrapped version appear to be the best choices for selection and quantifying uncertainty with confidence intervals and
-values.
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